Draft dodgers! There's the motive. People against the Vietnam war, who thought America was on the wrong path, who didn't want to do their fair share, who thought too much was being demanded of them... so they left and tried to convince everyone they were right for doing so.
I've looked at Catholicism/Protestantism as Jews/Samaritans, but I think there's an analogy in our own country as well. The president is nuts, many of us can barely bring ourselves to even refer to the man who holds the office as president, the congress is nuts, the Supreme Court is nuts, the states are nuts... the country is in a shambles. Do we go off and start a "pure US" somewhere else anointing ourselves President/Speaker/Chief Justice?
Anyhow, one motive of people who schism is to legitimize their own position by convincing others. In some social situations it's ok to do that.
To answer your question, no, we don't go off and start a "pure US" somewhere else anointing ourselves President/Speaker/Chief Justice. Instead, we clean out the wrong-headed leaders, and return the country to its original ideals, much like the reformers tried to do to "The Church". It had lost its way and had been perverted by evil men.